Is it possible to avoid the need for anodes by simply disconnecting shorepower and batteries while at the dock? Or is the mere presence of dissimilar metals in water enough to case a problem? Thanks, all advice greatly appreciated.
While most corrosion issues are due to electrical issues aboard the boat in question; your neighbor's boat can have problems that affect you whether or not you are plugged into shorepower. And disconnecting your battery means no bilge pump, thereby risking the entire boat. And yes, galvanic corrosion is always an issue. So the short answer is, "No, unless you have no underwater metal parts, you cannot avoid the need for anodes."
Zincs are relatively cheap insurance. Why would you even consider trying to forgo that small expense?